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src/Modal/s43.thy
author wenzelm
Thu Aug 27 20:46:36 1998 +0200 (1998-08-27)
changeset 5400 645f46a24c72
parent 0 a5a9c433f639
permissions -rw-r--r--
made tutorial first; 
     1 (*  Title: 	91/Modal/S43

     2     ID:         $Id$

     3     Author: 	Martin Coen

     4     Copyright   1991  University of Cambridge

     5 

     6 This implements Rajeev Gore's sequent calculus for S43.

     7 *)

     8 

     9 S43 = Modal0 +

    10 

    11 consts

    12   S43pi	:: "[sobj=>sobj, sobj=>sobj, sobj=>sobj,\

    13 \	     sobj=>sobj, sobj=>sobj, sobj=>sobj] => prop"

    14   "@S43pi" :: "[sequence, sequence, sequence, sequence, sequence,\

    15 \		sequence] => prop" ("S43pi((_);(_);(_);(_);(_);(_))" [] 5)

    16 

    17 rules

    18 (* Definition of the star operation using a set of Horn clauses  *)

    19 (* For system S43: gamma * == {[]P | []P : gamma}                *)

    20 (*                 delta * == {<>P | <>P : delta}                *)

    21 

    22   lstar0         "|L>"

    23   lstar1         "$G |L> $H ==> []P, $G |L> []P, $H"

    24   lstar2         "$G |L> $H ==>   P, $G |L>      $H"

    25   rstar0         "|R>"

    26   rstar1         "$G |R> $H ==> <>P, $G |R> <>P, $H"

    27   rstar2         "$G |R> $H ==>   P, $G |R>      $H"

    28 

    29 (* Set of Horn clauses to generate the antecedents for the S43 pi rule       *)

    30 (* ie                                                                        *)

    31 (*           S1...Sk,Sk+1...Sk+m                                             *)

    32 (*     ----------------------------------                                    *)

    33 (*     <>P1...<>Pk, $G |- $H, []Q1...[]Qm                                    *)

    34 (*                                                                           *)

    35 (*  where Si == <>P1...<>Pi-1,<>Pi+1,..<>Pk,Pi, $G * |- $H *, []Q1...[]Qm    *)

    36 (*    and Sj == <>P1...<>Pk, $G * |- $H *, []Q1...[]Qj-1,[]Qj+1...[]Qm,Qj    *)

    37 (*    and 1<=i<=k and k<j<=k+m                                               *)

    38 

    39   S43pi0         "S43pi $L;; $R;; $Lbox; $Rdia"

    40   S43pi1

    41    "[| (S43pi <>P,$L';     $L;; $R; $Lbox;$Rdia);   $L',P,$L,$Lbox |- $R,$Rdia |] ==> \

    42 \       S43pi     $L'; <>P,$L;; $R; $Lbox;$Rdia"

    43   S43pi2

    44    "[| (S43pi $L';; []P,$R';     $R; $Lbox;$Rdia);  $L',$Lbox |- $R',P,$R,$Rdia |] ==> \

    45 \       S43pi $L';;     $R'; []P,$R; $Lbox;$Rdia"

    46 

    47 (* Rules for [] and <> for S43 *)

    48 

    49   boxL           "$E, P, $F, []P |- $G ==> $E, []P, $F |- $G"

    50   diaR           "$E |- $F, P, $G, <>P ==> $E |- $F, <>P, $G"

    51   pi1

    52    "[| $L1,<>P,$L2 |L> $Lbox;  $L1,<>P,$L2 |R> $Ldia;  $R |L> $Rbox;  $R |R> $Rdia;  \

    53 \      S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==> \

    54 \   $L1, <>P, $L2 |- $R"

    55   pi2

    56    "[| $L |L> $Lbox;  $L |R> $Ldia;  $R1,[]P,$R2 |L> $Rbox;  $R1,[]P,$R2 |R> $Rdia;  \

    57 \      S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==> \

    58 \   $L |- $R1, []P, $R2"

    59 end

    60 

    61 ML

    62 

    63 local

    64 

    65   val S43pi  = "S43pi";

    66   val SS43pi = "@S43pi";

    67 

    68   val tr  = LK.seq_tr1;

    69   val tr' = LK.seq_tr1';

    70 

    71   fun s43pi_tr[s1,s2,s3,s4,s5,s6]=

    72 	Const(S43pi,dummyT)$tr s1$tr s2$tr s3$tr s4$tr s5$tr s6;

    73   fun s43pi_tr'[Abs(_,_,s1),Abs(_,_,s2),Abs(_,_,s3),

    74 		Abs(_,_,s4),Abs(_,_,s5),Abs(_,_,s6)] =

    75         Const(SS43pi,dummyT)$tr' s1$tr' s2$tr' s3$tr' s4$tr' s5$tr' s6;

    76 in

    77 val parse_translation = [(SS43pi,s43pi_tr)];

    78 val print_translation = [(S43pi,s43pi_tr')]

    79 end
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